Abstractions from Precipitation | Engineering Hydrology - Civil Engineering (CE) PDF Download

Evaporation and its Measurement

Evaporation is a cooling process in which the latent heat of evaporation of about 585 cal/gm is provided by the water body. in this process liquid changes into gaseous phase at free surface, below the boiling point through the transfer of heat energy.

Dalton’s Law
The rate of evaporation is proportional to the difference between the saturation vapour pressure at the water temperature, e_s and the actual vapour pressure in the air e_a thus
E = K(e_s - e_a)
Where, E = Rate if evaporation (mm/day)
e_s = Saturation vapour pressure of air (mm)
e_a = Actual vapour pressure of air (mm)
e_s - e_a Saturation deficiency

Measurement of Evaporation

1. ISI standard pan
   Lake evaporation = C_p × pan evaporation
   Where, C_p pan coefficient
   = 0.8 for ISI pan
   = 0.7 for class A-Pan
2. Empirical Evaporation Equations (Meyer’s Formula) E = k_m(e_s - e_a)[1 + (V₉ / 16]
   Where, k_m = Coefficients which accounts for size of water body.
   = 0.36 (for large deep water)
   ∼ 0.50 (for small and shallow waters)
   e_s = Saturation vapour pressure of air in mm of Hg.
   e_a = Actual vapour pressure of overlying air in mm at Hg at specified height of 8 m.
   V₉ = monthly mean wind velocity in km/hr at about 9 m above the ground level.

1/7th power Law
V₁ / V₂ = (H₁ / H₂)^1/7
Where, V₁ is the wind velocity at height H₁ and V₂ is the wind velocity at height H₂.

Water Budget Method
This is simplest method bit it is least reliable it is used for rough calculation, it is based on mass conversation principle.
P + V_is + V_ig + V_og + E + ΔS + T_L
Where, P=Daily precipitation on the water surface.
V_is = Daily surface inflow into take.
V_os = Daily surface outflow from lake.
V_ig = Daily underground inflow into the lake.
V_og = Daily underground outflow from the lake.
E = Daily Evaporation
ΔS = change in storage of lake
= +ve if increase in storage
= -ve if decrease in storage
T_L = Daily transpiration loss from the plants on the lake.

Energy Budget Method
The energy budget method is an application of the law of conservation of energy. The energy available for evaporation is determined by considering the incoming energy. Outgoing energy and energy stored in the water body over a known time interval.

Where, H_n = Net heat energy received by the water surface
H_n = H_c(1 - r) - H_b
H_c(1 - r) = incoming solar radiation into a surface of reflection coefficient, r
H_b = Back radiation from water body
H_g = Heat flux into the ground
H_S = Heat stored in water body
H_i = Net heat conducted out the system by water flow (advected energy)
β = Bowen’s ratio
δ = Density of water
L = Latent heat of evaporation.

Evapo-Transpiration
While transpiration takes place, the land are in which plants stand also lose moisture by the evaporation of water from soil and water bodies. In hydrology and irrigation practive, it is found that evaporation and transpiration processes can be considered advantageously under one head as evapo-transpiration.
The real evapo-transpiration occurring in a specific situation is called actual evapo-transpiration (AET).

Penman’s Method

Penman’s equation is based on sound theoretical reasoning and is obtained by a combination of the energy balance and mass transfer approach.

Where, PET = daily evaporation in mm/day.
A = slope of the saturation vapour pressure v/s temperature curve at the mean air temperature in mm of Hg per °C.
H_n = Net radiation in mm of evaporable water per day
E_a = Parameter including wind velocity and saturation deficit.
γ = Psychometric constant
= 0.49 mm of Hg/°C
It is based on mass transfer and energy balance.

Transpiration Loss (T)
T = (w₁ + w₂) - w₂
Where, w₁ = Initial weight of the instrument
W = Total weight of water added for full growth of plant.
w₂ = Final weight of instruction including plant and water
T = Transpiration loss.

Stream Flow Measurement
Streamflow representing the runoff phase of the hydrologic cycle is the most important basic data for hydrologic studies.
Streamflow measurement techniques can be broadly classified into two categories as:

• Direct determination and
• Indirect determination.

Under each category there are a host of methods. The important ones are listed below:

1. Direct determination of stream discharge
   (a) Area velocity methods
   (b) Dilution techniques
   (c) Electromagnetic method and
   (d) ultrasonic method
2. Indirect determination of streamflow
   (a) Hydraulic structures, such as weirs, flumes and gated structures, and
   (b) Slope- area method

Determination of Velocity

1. Float Method: Float are generally used to determine approximate velocity of the surface, these are floating devices which are passed with the water along the flow of stream.
   V_s = L / t Here, V_s = surface velocity
   L= Distance travelled by the float in time ‘t’.
2. Current Meters Method: These consists of rotating elements which rotate due to reactions of stream currents. The number of revolution per second are counted. This can be used to measure point velocity of ant depth.
   V = aN_s + b
   Where, V = point velocity
   N_s = Number of revolution per sec. a and b are current meters constant.

Velocity Distribution

1.  
   For turbulent flow
   Where, mean velocity
   V_s = surface velocity
2. For shallow streams
    where  point velocity at 0.6 y from surface 
3. For Deep streams  
   Sounding Weight
    W = weight in newton 
   Average stream velocity 
   Y = Depth of flow in meters.

Stream Flow (discharge measurement)

1. Area Velocity Method: This method of discharge measurement consists essentially of measuring the area of cross-section of the river at a selected section called the gauging site and measuring the velocity of flow through the cross-sectional area. The gauging site must be selected with care to assure that the stage-discharge curve is reasonably constant over a long period of about a few years.
   Total discharge,
    
   
2. Moving Boat Method: in this method a special propeller type current meter which is free to move about a vertical axis is towed in a boat at a velocity V_B at right angles to stream flow. If the flow velocity is V_F the meter will align itself in the direction of the resultant velocity V_R making an angle θ with the direction of the boat. Further. The meter will ragister the velocity V_R if V_B IS normal VF.
   V_B = V_Rcosθ
   V_F=V_Rsinθ
   
   Where, qi = Discharge through the i^th segment.
   q_i = ((Y_i-1 + y_i) / 2)V²R sinθ.cosθ.t_i
   t_i = Time required to pass the boat through i^th segment.
3. Dilution Method: the dilution method of flow measurement, also known as the chemical method depends upon the continuity principle applied to a tracer which is allowed to mix completely with the flow.
   
   This technique in which Q₀ is estimated by knowing C₁, C₂, C₀ and Q₁ is known as constant rate injection method or plateau gauging.
   Where,
   Q₀ = Discharge of stream
   C₀ = Tracer intensity initially
   C₁ = Tracer intensity at (1)
   C₂ = Tracer intensity at (2).
   Q₁ and Q₂ are discharge at (1) and (2) respectively.
4. Slope Area Method: it is a very versatile indirect method of discharge estimation and requires
   (i) the selection of a reach in which cross-sectional properties including bed elevations are known at its ends.
   (ii) the value of Manning’s n and
   (iii) water-surface elevations at the two end sections.
   (a)Where H_f = Frictional losses
   H_e = Eddy losses
   (b)
   k_e = Eddy loss coefficients.
   (c)
   (d)
   (e)  Where, Q = stream flow (m³/sec) 
   (f) k = (k₁ . k₂... k_n)^1/n Where, k = Conveyance 
   (g) k = 1/n . A . R^2/3 Where, A = area (m²)
   R = Hydraulic mean depth
   = Area / wetted perimeter